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A111812 Column 3 of triangle A098539, which shifts columns left and up under matrix square.

%I A111812 #4 Mar 30 2012 18:36:50
%S A111812 1,8,72,888,16392,479736,23196168,1909718520,273790460424,
%T A111812 69532461669880,31699923943776776,26220200137673186808,
%U A111812 39689067731528646091272,110732781183212424923225592
%N A111812 Column 3 of triangle A098539, which shifts columns left and up under matrix square.
%F A111812 G.f.: A(x) = 1 + Sum_{n>=1} 8^n/n!*Product_{j=0..n-1} L(2^j*x) where L(x) = e.g.f. of A111811 (column 0 of matrix log of A098539) satisfies: x = L(x) - L(x)*L(2*x)/2! + L(x)*L(2*x)*L(2^2*x)/3! - L(x)*L(2*x)*L(2^2*x)*L(2^3*x)/4! + ...
%e A111812 A(x) = 1 + 8*x + 72*x^2 + 888*x^3 + 16392*x^4 + 479736*x^5 +...
%o A111812 (PARI) {a(n,q=2)=local(A=Mat(1),B);if(n<0,0, for(m=1,n+4,B=matrix(m,m);for(i=1,m, for(j=1,i, if(j==i,B[i,j]=1,if(j==1,B[i,j]=(A^q)[i-1,1], B[i,j]=(A^q)[i-1,j-1]));));A=B);return(A[n+4,4]))}
%Y A111812 Cf. A098539, A111811.
%K A111812 nonn
%O A111812 0,2
%A A111812 _Paul D. Hanna_, Aug 22 2005